Skip to main content
Log in

Dynamical modelling and control of space tethers: a review of space tether research

  • Review
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

The literature review manuscript focuses mainly on five topics, which are related to the space tether control researches: (1) space tether dynamical modelling; (2) tether deployment and retrieval; (3) trajectory generation and control; (4) tether attitude and motion control; (5) tether vibration control and dynamical simulations. With the basic aim of establishing useful sources of fundamental researches in the literature, and high-lighting the previous control methods developed, this paper attempts to provide a contextualised source of references for the further space tether dynamics and control studies.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Logsdon, T.: Orbital Mechanics: Theory and Applications. Wiley, New York (1997)

    Google Scholar 

  2. Curtis, H.: Orbital Mechanics for Engineering Students. Elsevier Science Aerospace Engineering Series. Butterworth-Heinemann, Burlington (2004)

    Google Scholar 

  3. Roy, A.E., Clarke, D.: Astronomy: Principles and Practice, 4th edn. Taylor and Francis, London (2003)

    Google Scholar 

  4. Chen, Y.: Dynamical modelling of a flexible motorised momentum exchange tether and hybrid fuzzy sliding mode control for spin-up. PhD Thesis, Department of Mechanical Engineering, University of Glasgow, Glasgow (2010)

  5. Cartmell, M.P., McKenzie, D.J.: A review of space tether research. Prog. Aerosp. Sci. 44, 1–21 (2008)

    Google Scholar 

  6. Sorensen, K.: Momentum exchange electrodynamic reboost (MXER) tether. National Aeronautics and Space Administration, Marshall Space Flight Center Technical, Report FS-2005-05-61-MSFC, 8–40407 (2005)

  7. Misra, A.K., Modi, V.J.: Dynamics and control of tether connected two-body systems - a brief review. The 33rd International Astronautical Federation, International Astronautical Congress, Paris, France, 27 September - 2 October, 219–236 (1982)

  8. Misra, A.K., Modi, V.J.: A survey on the dynamics and control of tethered satellite systems. NASA/AIAA/PSN International Conference on Tethers, Arlington, VA, 17–19 September (1986)

  9. Eiden, M.J., Cartmell, M.P.: Overcoming the challenges: tether systems roadmap for space transportation applications. AIAA/ICAS International Air and Space Symposium and Exposition, Dayton Convention Center, Dayton, Ohio, 14–17 July (2003)

  10. Kumar, K.D.: Review of dynamics and control of nonelectrodynamic tethered satellite systems. J. Spacecr. Rockets 43, 705–720 (2006)

    Google Scholar 

  11. Chen, Y., Huang, R., Ren, X.-L., He, L.-P., He, Y.: History of the tether concept and tether missions: a review. ISRN Astron. Astrophys. 502973, 7 (2013)

    Google Scholar 

  12. Cosmo, M.L., Lorenzini, E.C.: Tethers in Space Handbook (third edition). NASA Marshall Space Flight Center, Huntsville (1997)

    Google Scholar 

  13. Kelly, W.D.: Delivery and disposal of a space shuttle external tank to low-earth orbit. J. Astronaut Sci. 32, 343–350 (1984)

    Google Scholar 

  14. Bilen, S.G.: Space-borne tethers. IEEE Potentials 13, 47–50 (1994)

    Google Scholar 

  15. DeCou, A.B.: Tether static shape for rotating multimass, multitether, spacecraft for triangle michelson interferometer. J. Guid. 12, 273–275 (1989)

    Google Scholar 

  16. Kumar, K., Kumar, R., Misra, A.K.: Effects of deployment rates and librations on tethered payload raising. J. Guid. Control Dyn. 15, 1230–1235 (1992)

    Google Scholar 

  17. Vigneron, F.R., Jablonski, A.M., Chandrashaker, R., Bergmans, J.L., McClure, B.A., Tyc, G.: Comparison of analytical modelling of oedipus tethers with data from tether laboratory. J. Guid. Control Dyn. 20, 471–478 (1997)

    Google Scholar 

  18. Cartmell, M.P.: Generating velocity increments by means of a spinning motorised tether. 34th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Cleveland Conference Centre, Cleveland, Ohio, USA, AIAA-98-3739 (1998)

  19. Cartmell, M.P., Ziegler S.W.: Experimental Scale Model Testing of a Motorised Momentum Exchange Propulsion Tether. 37th AIAA/ASME/SEA/ASEE Joint Propulsion Conference and Exhibit, July 8–11, Salt Lake City, Utah, USA, AIAA 2001–3914 (2001)

  20. Cartmell, M.P., Ziegler S.W., Neill, D.S.: On the Performance Prediction and Scale Modelling of A Motorised Momentum Exchange Propulsion Tether. 20th Symposium Space Nuclear Power and Propulsion; Space technology and applications international forum 2003, 2–5 February, University of New Mexico, Albuquerque, New Mexico, USA (2003)

  21. Ziegler, S.W., Cartmell, M.P.: Using motorised tethers for payload orbital transfer. J. Spacecr. Rockets 38, 904–913 (2001)

    Google Scholar 

  22. Chen, Y., Cartmell, M.P.: Multi-objective optimisation on motorized momentum exchange tether for payload orbital transfer. 2007 IEEE Congress on Evolutionary Computation (CEC), Singapore, 25–28 September (2007)

  23. Chen, Y., Cartmell, M.P.: Dynamical modelling of the motorised momentum exchange tether incorporating axial elastic effects. Advanced Problems in Mechanics Conference, Russian Academy of Sciences, St. Petersburg, Russia, 20–28 June (2007)

  24. Chen, Y., Cartmell, M.P.: Hybrid fuzzy and sliding-mode control for motorised tether spin-up when coupled with axial vibration. The 7th International Conference on Modern Practice in Stress and Vibration Analysis, New Hall, Cambridge, UK, 8–10 September (2009)

  25. Chen, Y., Cartmell, M.P.: Hybrid sliding mode control for motorised space tether spin-up when coupled with axial oscillation. Advanced Problems in Mechanics Conference, St Petersburg, Russia, 30 June-5 July (2009)

  26. Chen, Y., Cartmell, M.P.: Hybrid sliding mode control for motorised space tether spin-up when coupled with axial and torsional oscillation. Astrophys. Space Sci. 326, 105–118 (2010)

    Google Scholar 

  27. Ziegler, S.W.: the Rigid-body Dynamics of Tethers in Space, PhD Dissertation. Department of Mechanical Engineering, University of Glasgow (2003)

  28. McKenzie, D.J.: The dynamics of tethers and space-webs. PhD Thesis, Mechanical Engineering Department, University of Glasgow, Glasgow (2010)

  29. Murray, C.: Continuous Earth-Moon payload exchange using motorised tethers with associated dynamics. PhD Thesis, Mechanical Engineering Department, University of Glasgow, Glasgow (2011)

  30. Ismail, N.A.: The dynamics of a flexible Motorised Momentum Exchange Tether (MMET), PhD Thesis, Mechanical Engineering Department, University of Glasgow, Glasgow (2012)

  31. Mazzoleni, A.P., Hoffman, J.H.: Nonplanar spin-up dynamics of the astor tethered satellite system. In: Proceedings of the 2001 AAS/AIAA Space Flight Mechanics Meeting, AAS 01–193 (2001)

  32. Mazzoleni, A.P., Hoffman, J.H.: End-body dynamics of artificial gravity generating tethered satellite system during non-planar spin-up with elastic effects included. Adv. Astronaut. Sci. 116, 579–694 (2003)

    Google Scholar 

  33. Ellis, J.R., Hall, C.D.: Out-of-plane librations of spinning tethered satellite systems. Celest. Mech. Dyn. Astron. 106, 39–67 (2010)

    MATH  MathSciNet  Google Scholar 

  34. Aslanov, V.S.: The effect of the elasticity of an orbital tether system on the oscillations of a satellite. J. Appl. Math. Mech. 74, 416–424 (2010)

    MATH  MathSciNet  Google Scholar 

  35. Zanutto, D., Curreli, D., Lorenzini, E.C.: Stability of electrodynamic tethers in a three-body system. J. Guid. Control Dyn. 34, 1441–1456 (2011)

    Google Scholar 

  36. Kristiansen, K.U., Palmer, P.L., Roberts, R.M.: Numerical modelling of elastic space tethers. Celest. Mech. Dyn. Astron. 113, 235–254 (2012)

    MathSciNet  Google Scholar 

  37. Zhao, G.W., Sun, L., Tan, S.P., Huang, H.: Librational characteristics of a dumbbell modeled tethered satellite under small, continuous, constant thrust. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 1–16 (2012)

  38. Jung, W.Y., Mazzoleni, A.P., Chung, J.T.: Dynamic analysis of a tethered satellite system with a moving mass. Nonlinear Dyn. 75, 267–281 (2014)

    MathSciNet  Google Scholar 

  39. Tomlin, D.D., Faile, G.C., Hayashida, K.B., Frost, C.L., Wagner, C.Y., Mitchell, M.L., Vaughn, J.A., Galuska, M.J.: Space tethers: design criteria. NASA Center: Marshall Space Flight Center Technical Report, Alabama, NASA Technical Memorandum 108537 (1997)

  40. Hoyt, R.P., Forward, R.L.: Cislunar tether transport system. The 38th Aerospace Sciences Meeting and Exhibit, 10–13 January, Reno, Nevada, AIAA 00–0329 (2000)

  41. Hoyt, R.P.: Moon and mars orbiting spinning tether transport system architecture study. Final Report on NASA Institute for Advanced Concepts Contract 07600–034 (2001)

  42. Kumar, K.D.: Payload deployment by reusable launch vehicle using tether. J. Spacecr. Rockets 38, 291–294 (2001)

    Google Scholar 

  43. Williams, P., Blanksby, C., Trivailo, P.: Tethered planetary capture: controlled maneuvers. Acta Astronaut. 53, 681–708 (2003)

    Google Scholar 

  44. Williams, P., Yeo, S., Blanksby, C.: Heating and modeling effects in tethered aerocapture missions. J. Guid. Control Dyn. 26, 643–654 (2003)

    Google Scholar 

  45. Williams, P., Blanksby, C., Trivailo, P.: Tethered planetary capture maneuvers. J. Spacecr. Rockets 41, 603–613 (2004)

    Google Scholar 

  46. Williams, P., Blanksby, C., Trivailo, P.: Libration control of flexible tethers using electromagnetic forces and movable attachment. J. Guid. Control Dyn. 27, 882–897 (2004)

    Google Scholar 

  47. Williams, P., Blanksby, C.: Prolonged payload rendezvous using a tether actuator mass. J. Spacecr. Rockets 41, 889–892 (2004)

    Google Scholar 

  48. Williams, P., Blanksby, C., Trivailo, P., Fujii, H.A.: In-plane payload capture using tethers. Acta Astronaut. 57, 772–787 (2005)

    Google Scholar 

  49. Williams, P.: Optimal orbit transfer with electrodynamic tether. J. Guid. Control Dyn. 28, 369–372 (2005)

    Google Scholar 

  50. Williams, P.: Dynamics and control of spinning tethers for rendezvous in elliptic orbits. J. Vib. Control 12, 737–771 (2006)

    MATH  MathSciNet  Google Scholar 

  51. Modi, V.J., Misra, A.K.: On the deployment dynamics of tether connected two-body systems. Acta Astronaut. 6, 1183–1197 (1979)

    Google Scholar 

  52. Bergamaschi, S., Bonon, F., Merlina, P., Morana, M.: Theoretical and experimental investigation of TSS-1 dynamics. Acta Astronaut. 34, 69–82 (1994)

    Google Scholar 

  53. Chernousko, F.L.: Dynamics of retrieval of a space tethered system. J. Appl. Math. Mech. 59, 165–173 (1995)

    MathSciNet  Google Scholar 

  54. Pelaez, J.: On the dynamics of the deployment of a tether from an orbiter-I. Basic equations. Acta Astronaut. 36, 113–122 (1995)

    Google Scholar 

  55. Pelaez, J.: On the dynamics of the deployment of a tether from an orbiter-part II. Exponential deployment. Acta Astronaut. 36, 313–335 (1995)

    Google Scholar 

  56. Koss, S.: Tether Deployment Mechanism for the Advanced Tether Experiment (ATEX). European Space Mechanism and Tribology Symposium 175–182 (1997)

  57. Licata, R.: Tethered system deployment controls by feedback fuzzy logic. Acta Astronaut. 40, 619–634 (1997)

    Google Scholar 

  58. Carter, J. T., Greene, M.: Deployment and Retrieval Simulation of a Single Tether Satellitesystem. Proceedings of the Twentieth Southeastern Symposium 657–660 (1988)

  59. Kumar, K., Pradeep, S.: Strategies for three dimensional deployment of tethered satellites. Mech. Res. Commun. 25, 543–550 (1998)

    MATH  MathSciNet  Google Scholar 

  60. Campbell, M.E., How, J.P., Grocott, S., Miller, D.W.: On-orbit closed-loop control results for the middeck active control experiment. J. Guid. Control Dyn. 22, 267–277 (1999)

    Google Scholar 

  61. Djebli, A., Pascal, M., Bakkali, L.: Laws of deployment/retrieval in tether connected satellites systems. Acta Astronaut. 45, 61–73 (1999)

    Google Scholar 

  62. Djebli, A., Bakkali, L., Pascal, M.: On fast retrieval laws for tethered satellite systems. Acta Astronaut. 50, 461–470 (2002)

    Google Scholar 

  63. Barkow, B.: Controlled deployment of a tethered satellite system. Proc. Appl. Math. Mech. 2, 224–225 (2003)

    Google Scholar 

  64. Barkow, B., Steindl, A., Troger, H., Wiedermann, G.: Various methods of controlling the deployment of a tethered satellite. J. Vib. Control 9, 187–208 (2003)

    MATH  MathSciNet  Google Scholar 

  65. Barkow, B., Steindl, A., Troger, H.: A targeting strategy for the deployment of a tethered satellite system. J. Appl. Math. 70, 626–644 (2005)

    MATH  MathSciNet  Google Scholar 

  66. Jin, D.P., Hu, H.Y.: Optimal control of deployment of a tethered subsatellite. Nonlinear Dyn. 31, 257–274 (2003)

    Google Scholar 

  67. Steindl, A., Steiner, W., Troger, H.: Optimal control of retrieval of a tethered subsatellite. IUTAM symposium on chaotic dynamics and control of systems and processes in mechanics 441–450 (2005)

  68. Gl\(\ddot{a}\beta \)el, H., Zimmermann, F., Br\(\ddot{u}\)ckner, S., Sch\(\ddot{o}\)ttle, U.M., Rudolph, S.: Adaptive neural control of the deployment procedure for tether-assisted re-entry. Aerosp. Sci. Technol. 8, 73–81 (2004)

  69. Jin, D.P., Hu, Y.: Optimal control of a tethered subsatellite of three degrees of freedom. Nonlinear Dyn. 46, 161–178 (2006)

    MATH  MathSciNet  Google Scholar 

  70. Williams, P.: Optimal deployment/retrieval of a tethered formation spinning in the orbital plane. J. Spacecr. Rockets 43, 638–650 (2006)

    Google Scholar 

  71. Williams, P.: Optimal deployment/retrieval optimization for flexible tethered satellite systems. Nonlinear Dyn. 52, 159–179 (2008)

    MATH  Google Scholar 

  72. Mantri, P.: Deployment Dynamics of Space Tether Systems. PhD thesis, North Carolina State University (2007)

  73. Iki, K., Kawamoto, S., Morino, Y.: Experiments and numerical simulations of an electrodynamic tether deployment from a spool-type reel using thrusters. Acta Astronaut. 94, 318–327 (2014)

    Google Scholar 

  74. Modi, V.J.: On the semi-passive attitude control and propulsion of space vehicles using solar radiation pressure. Acta Astronaut. 35, 231–246 (1995)

    Google Scholar 

  75. Nohmi, M., Nenchev, D.N., Uchiyama, M.: Trajectory planning and feedforward control of a tethered robot system. Proc. IEEE/RSJ Int. Conf. Intell. Robots Syst. 3, 1530–1535 (1996)

    Google Scholar 

  76. Cao, Y., Modi, V.J., Silva, C.W., Chu, M., Chen, Y., Misra, A.K.: Trajectory tracking experiments using a novel manipulator. Acta Astronaut. 52, 523–540 (2003)

    Google Scholar 

  77. Aaron, K.M., Heun, M.K., Nock, K.T.: A method for balloon trajectory control, advances in space research. Adv. Space Res. 30, 1227–1232 (2002)

    Google Scholar 

  78. Milam, M.B.: Real-time optimal trajectory generation for constrained dynamical systems, PhD thesis, California Institute of Technology (2003)

  79. Sakamoto, Y., Yasaka, Y.: Methods for the orbit determination of a tethered satellite system by a single ground station. Mem. Fac. Eng. Kyushu Univ. 63, 185–202 (2003)

    Google Scholar 

  80. Takeichi, N., Natori, M.C., Okuizumi, N., Higuchi, K.: Periodic solutions and controls of tethered systems in elliptic orbits. J. Vib. Control 10, 1393–1413 (2004)

    Google Scholar 

  81. Kim, M.: Continuous low-thrust trajectory optimization: techniques and applications. PhD thesis, Virginia Polytechnic Institute and State University (2005)

  82. Anselmo, L., Pardini, C.: The survivability of space tether systems in orbit around the earth. Acta Astronaut. 56, 391–396 (2005)

    Google Scholar 

  83. Padgett, D.A.: Nullcline analysis as a tethered satellite mission design tool. Master thesis, North Carolina State University (2006)

  84. Sharma, S., Kulczycki, E.A., Elfes, A.: Trajectory generation and path planning for autonomous aerobots. IEEE International Conference on Robotics and Automation 10–14 (2007)

  85. Williams, P., Hyslop, A., Stelzer, M., Kruijff, M.: YES2 optimal trajectories in presence of eccentricity and aerodynamic drag. Acta Astronaut. 64, 745–769 (2009)

    Google Scholar 

  86. Nakanishi, K., Kojima, H., Watanbe, T.: Trajectories of in-plane periodic solutions of tethered satellite system projected on Van Ser Pol planes. Acta Astronaut. 68, 1024–1030 (2011)

    Google Scholar 

  87. Avanzini, G., Fedib, M.: Refined dynamical analysis of multi-tethered satellite formations. Acta Astronaut. 84, 36–48 (2013)

    Google Scholar 

  88. Zhao G.W., Sun, L., Huang. H.: Thrust control of tethered satellite with a short constant tether in orbital maneuvering. Proceedings of the institution of mechanical engineers, Part G: J. Aerosp. Eng. 0954410014521151 (2014)

  89. Sun, L., Hedengren, J.D., Beard, R.W.: Optimal trajectory generation using model predictive control for aerially towed cable systems. J. Guid. Control Dyn. 37, 525–539 (2014)

    Google Scholar 

  90. Modi, V.J., Misra, A.K.: Dynamics of an array formed by three neutrally buoyant cylindrical cantilevers subjected to tensile follower forces. J. Sound Vib. 42, 209–217 (1975)

    MATH  Google Scholar 

  91. Bainum, P.M., Kumar, V.K.: Optimal control of the shuttle-tethered-subsatellite system. Acta Astronaut. 7, 1333–1348 (1980)

    MATH  Google Scholar 

  92. Modi, V.J., Xu, D., Misra, A.K., ChangFu, G.: On the control of the space shuttle based tethered systems. Acta Astronaut. 9, 437–443 (1982)

    Google Scholar 

  93. Misra, A.K., Amier, Z., Modi, V.J.: Attitude dynamics of three-body tethered systems. Acta Astronaut. 17, 1059–1068 (1988)

    MATH  Google Scholar 

  94. Modi, V.J.: Spacecraft attitude dynamics: evolution and current challenges. Acta Astronaut. 21, 669–718 (1990)

    Google Scholar 

  95. Lea, R.N., Villarreal, J., Jani, Y., Copeland, C.: Tether Operations using fuzzy logic based length control. IEEE International Conference on Fuzzy Systems 1335–1342 (1992)

  96. Modi, V.J., Lakshmanan, P.K.: On the control of tethered satellite systems. Acta Astronaut. 26, 411–423 (1992)

    Google Scholar 

  97. Modi, V.J., Pidgeon, R.P.: Dynamics and control of a flexible tethered system with offset. Acta Astronaut. 32, 255–265 (1994)

    Google Scholar 

  98. Grassi, M., Moccia, A., Vetrella, S.: Tethered system attitude control after attachment point blocking. Acta Astronaut. 32, 355–362 (1994)

    Google Scholar 

  99. Grassi, M., Cosmo, M.L.: Attitude dynamics of the small expendable-tether deployment system. Acta Astronaut. 36, 141–148 (1995)

    Google Scholar 

  100. Modi, V.J., Pradhan, S., Misra, A.K.: Off-set control of the tethered systems using a graph theoretic approach. Acta Astronaut. 35, 373–384 (1995)

    Google Scholar 

  101. Modi, V.J., Pradhan, S., Chu, M., Tyc, G., Misra, A.K.: Experimental investigation of the dynamics of spinning tethered bodies. Acta Astronaut. 39, 487–495 (1996)

    Google Scholar 

  102. Pasca, M., Lorenzini, E.C.: Two analytical models for the analysis of a tethered satellite system in atmosphere. Acta Astronaut. 39, 263–277 (1997)

    MathSciNet  Google Scholar 

  103. Modi, V.J., Pradhan, S., Misra, A.K.: Controlled dynamics of flexible orbiting tethered systems: analysis and experiments. J. Vib. Control 3, 459–497 (1997)

    MATH  MathSciNet  Google Scholar 

  104. Pradhan, S., Modi, V.J., Misra, A.K.: Tether-platform coupled control. Acta Astronaut. 44, 243–256 (1999)

    Google Scholar 

  105. Kumar, K., Kumar, K.D.: Tethered dual spacecraft configuration: a solution to attitude control problems. Aerosp. Sci. Technol. 4, 495–505 (2000)

    Google Scholar 

  106. Yu, S.: Tethered satellite system analysis (1)—two dimensional case and regular dynamics. Acta Astronaut. 3, 849–858 (2000)

    Google Scholar 

  107. Goulet, J.F., de Silva, C.W., Modi, V.J., Misra, A.K.: Hierarchical control of a space-based deployable manipulator using fuzzy logic. J. Guid. Control Dyn. 24, 395–405 (2001)

    Google Scholar 

  108. Kumar, K.D., Kumar, K.: Attitude maneuver of dual tethered satellite platforms through tether offset change. J. Spacecr. Rockets 38, 237–242 (2001)

    Google Scholar 

  109. Kim, M., Hall, C.: Control of a rotating variable-length tethered system. J. Guid. Control Dyn. 27, 849–858 (2004)

    Google Scholar 

  110. Lovera, M., Astolfi, A.: Spacecraft attitude control using magnetic actuators. Automatica 40, 1405–1414 (2004)

    MATH  MathSciNet  Google Scholar 

  111. Modi, V.J., Zhang, J., Silva, C.W.: Intelligent hierarchical modal control of a novel manipulator with slewing and deployable links. Acta Astronaut. 57, 761–771 (2005)

    Google Scholar 

  112. Guan, P., Liu, X., Liu, J.: Adaptive fuzzy sliding mode control for flexible satellite. Eng. Appl. Artif. Intell. 18, 451–459 (2005)

    Google Scholar 

  113. Zhou, X., Li, J., Baoyin, H., Zakirov, V.: Equilibrium control of electrodynamic tethered satellite systems in inclined orbits. J. Guid. Control Dyn. 29, 1451–1454 (2006)

    Google Scholar 

  114. Kim, M., Hall, C.: Dynamics and control of rotating tethered satellite systems. J. Spacecr. Rockets 44, 649–659 (2007)

    Google Scholar 

  115. Mori, O., Matunaga, S.: Formation and attitude control for rotational tethered satellite clusters. J. Spacecr. Rockets 44, 220–221 (2007)

    Google Scholar 

  116. Chung, S., Slotine, J.E., Miller, D.W.: Nonlinear model reduction and decentralized control of tethered formation flight by oscillation synchronization. J. Guid. Control Dyn. 30, 390–400 (2007)

    Google Scholar 

  117. Chung, S., Miller, D.W.: Propellant-free Control of tethered formation flight, part 1: linear control and experimentation. J. Guid. Control Dyn. 31(3), 571–584 (2008)

    Google Scholar 

  118. Chung, S., Slotine, J.E., Miller, D.W.: Propellant-free control of tethered formation flight, part 2: nonlinear underactuated control. J. Guid. Control Dyn. 31, 1437–1446 (2008)

    Google Scholar 

  119. Misra, A.K.: Dynamics and control of tethered satellite systems. Acta Astronaut. 31, 1437–1446 (2008)

    Google Scholar 

  120. Chang, L., Park, S.Y., Choi, K.H.: Nonlinear attitude control of a tether-connected multi-satellite in three-dimensional space. IEEE Trans. Aerosp. Electron. 46, 1950–1956 (2010)

    Google Scholar 

  121. Williams, P.: Optimal control of electrodynamic tether orbit transfers using timescale separation. J. Guid. Control Dyn. 33, 88–98 (2010)

    Google Scholar 

  122. Williams, P.: Electrodynamic tethers under forced-current variations part 1: periodic solutions for tether librations. J. Spacecr. Rockets 47, 308–319 (2010)

    Google Scholar 

  123. Williams, P.: Electrodynamic tethers under forced-current variations part 2: flexible-tether estimation and control. J. Spacecr. Rockets 47, 320–333 (2010)

    Google Scholar 

  124. Williams, P.: Quadrature discretization method in tethered satellite control. Appl. Math. Comput. 217, 8223–8235 (2011)

    MATH  MathSciNet  Google Scholar 

  125. Larsen, M.B., Blanke, M.: Passivity-based control of a rigid electrodynamic tether. J. Guid. Control Dyn. 34, 118–127 (2011)

    Google Scholar 

  126. He, L., Liang, B., Xu, W.F.: Study on the stability of tethered satellite system. Acta Astronaut. 68, 1964–1972 (2011)

    Google Scholar 

  127. Kojima, H., Sugimoto, Y., Furukawa, Y.: Experimental study on dynamics and control of tethered satellite systems with climber. Acta Astronaut. 69, 96–108 (2011)

    Google Scholar 

  128. Zhang, W., Gao, F.B., Yao, M.H.: Periodic solutions and stability of a tethered satellite system. Mech. Res. Commun. 44, 24–29 (2012)

    MATH  Google Scholar 

  129. Zabolotnov, Y.M., Naumov, O.N.: Motion of a descent capsule relative to its center of mass when deploying the orbital tether system. Cosmic Res. 20, 177–187 (2012)

    Google Scholar 

  130. I\(\tilde{n}\)arrea, M., Lanchares, V., Pascual, A.I., Salas, J.P.: Attitude stabilization of electrodynamic tethers in elliptic orbits by time-delay feedback control. Acta Astronaut. 96, 280–295 (2014).

  131. Zhong, R., Zhu, Z.H.: Optimal control of nanosatellite fast deorbit using electrodynamic tether. J. Guid. Control Dyn. 1–13 (2014).

  132. Tschann, C., Modi, V.J., Soudack, A.: Planar librations of gravity-oriented satellites using analog simulation. Math. Comput. Simul. 13, 124–130 (1971)

    Google Scholar 

  133. Lips, K.W., Modi, V.J.: Transient attitude dynamics of satellites with deploying flexible appendages. Acta Astronaut. 5, 797–815 (1978)

    MATH  Google Scholar 

  134. Misra, A.K., Xu, D.M., Modi, V.J.: On vibrations of orbiting tethers. Acta Astronaut. 3, 587–597 (1986)

    Google Scholar 

  135. Carter, J.T., Greene, M.: Simulation of single tether systems. Simulation 58, 42–48 (1992)

    Google Scholar 

  136. Kalantzis, S., Modi, V.J., Pradhan, S., Misra, A.K.: Dynamics and control of multibody tethered systems. Acta Astronaut. 42, 503–517 (1998)

    Google Scholar 

  137. Dignath, F., Schiehlen, W.: Control of the vibrations of a tethered satellite system. J. Appl. Math. Mech. 64, 715–722 (2000)

    Google Scholar 

  138. Leamy, M.J., Noor, A.K.: Dynamic simulation of a tethered satellite system using finite elements and fuzzy sets. Comput. Methods Appl. Mech. Eng. 190, 4847–4870 (2001)

    MATH  Google Scholar 

  139. Mouterde, E., Cartmell, M.P., Wang, Y.: Computational simulation of feedback linearised control of a motorised momentum exchange tether on a circular earth orbit. Nonlinear Dynamics, symposium of the sixth world congress on computational mechanics (2004)

  140. Williams, P.: Spacecraft rendezvous on small relative inclination orbits using tethers. J. Spacecr. Rockets 42, 1047–1060 (2005)

    Google Scholar 

  141. Krupa, M., Poth, W., Schagerl, M., Steindl, A., Steiner, W., Troger, H., Wiedermann, G.: Modelling, dynamics and control of tethered satellite systems. Nonlinear Dyn. 43, 73–96 (2006)

    MATH  MathSciNet  Google Scholar 

  142. Williams, P., Sgarioto, D., Trivailo, P.: Optimal control of an aircraft-towed flexible cable system. J. Guid. Control Dyn. 29, 401–410 (2006)

    Google Scholar 

  143. Williams, P.: Libration control of tethered satellites in elliptical orbits. J. Spacecr. Rockets 43, 476–479 (2006)

    Google Scholar 

  144. Valverde, J., Escalona, J.L., Domínguez, J., Champneys, A.R.: Stability and bifurcation analysis of a spinning space tether. J. Nonlinear Sci. 16, 507–542 (2006)

    MATH  MathSciNet  Google Scholar 

  145. Williams, P., Trivailo, P.: Dynamics of circularly towed aerial cable systems, part I: optimal configurations and their stability. J. Guid. Control Dyn. 30, 753–765 (2007)

    Google Scholar 

  146. Williams, P., Trivailo, P.: Dynamics of circularly towed aerial cable systems, part II: transitional flight and deployment control. J. Guid. Control Dyn. 30, 766–779 (2007)

    Google Scholar 

  147. Wen, H., Jin, D.P., Hu, H.Y.: Optimal feedback control of the deployment of a tethered subsatellite subject to perturbations. Nonlinear Dyn. 51, 501–514 (2008)

    MATH  MathSciNet  Google Scholar 

  148. Chen, Y.: SMATLINK—Simple Matlab and Mathematica link laboratory toolbox. http://www.mathworks.com/matlabcentral/fileexchange/20573 (2010). Accessed 10 March 2014

Download references

Acknowledgments

The authors would like to acknowledge the partial supports provided by the National Natural Science Foundation of China (No. 51105061, 61179059, 51305068 and 51275077), the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry (No. 201294001) and the Overseas Research Students Awards Scheme (ORSAS) awarded by the University of Glasgow and the scholarship awarded by the Faculty of Engineering, University of Glasgow. Also, the authors would like to acknowledge two anonymous reviewers with their valuable comments for this paper.

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Yi Chen or Bin Zheng.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chen, Y., Huang, R., He, L. et al. Dynamical modelling and control of space tethers: a review of space tether research. Nonlinear Dyn 77, 1077–1099 (2014). https://doi.org/10.1007/s11071-014-1390-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-014-1390-5

Keywords

Navigation